The weight of an object at the centre of the earth of radius $R$ is

Three students $A, B$ and $C$ were performing an experiment to establish the relation between the weight of a wooden block and the minimum force required to just move it on a horizontal surface. The experimental setup used by each is as shown in the figures given below.
The result obtained by them will be:

The gravitational force between two objects is $F$. How will this force change when:
$(i)$ the distance between them is reduced to half?
$(ii)$ the mass of one of the objects becomes four times?

The mass of a girl is $50\, kg$. What will be her approximate weight on the Earth? How will her mass and weight change on the surface of the Moon?

Suppose a planet exists whose mass and radius both are half that of Earth. Calculate the acceleration due to gravity on the surface of this planet.

State the universal law of gravitation. Write the $SI$ unit of $G$. The gravitational force between two objects is $100 \, N$. How should the distance between the objects be changed so that the force between them becomes $50 \, N$?